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Due to the non-locality of the clusters, the partition function Z(L,N) cannot be written simply as a trace of the transfer matrix T\\_L. Using a combinatorial method, we establish the decomposition Z(L,N) = \\sum\\_{l,D\\_k} b^{l,D\\_k} K\\_{l,D\\_k}, where the characters K\\_{l,D\\_k} = \\sum\\_i (\\lambda\\_i)^N are simple traces. 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